Most recipes don't call for using an entire can of tomato paste, which can be problematic if you don't plan on using any more of it for a while. An easy way to store any leftovers is to scoop them into 1-tablespoon dollops, wrap them in plastic wrap and freeze until solid. Once they're hard, you can stick them in a freezer bag (keep the plastic wrap around them), and store them in the freezer for up to 4-5 months. Get the full method here.